On the existence of a general rotating solution of Einstein's equations
- Jamal N. Islam
- … show all 1 hide
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
In an earlier paper we considered a power-series expansion of the metric for a rotating field in terms of a parameter and constructed a solution of Einstein's equations to the first few orders in terms of two harmonic functions. We encountered a pair of Poisson-type equations which were apparently insoluble explicitly. The form of the metric considered was the Weyl-Lewis-Papapetrou form. In this paper we consider a power-series expansion of the most general form of a rotating metric and show that one encounters the same two Poisson equations as before. If these equations are insoluble explicitly, as seems likely, then a general solution depending on two harmonic functions cannot exist in closed form.
- For a review of rotating solutions, see, e.g., Thorne, K. S. (1971). inGravitation and Cosmology, Proceedings of the International School of Physics Enrico Fermi Course 47 ed. Sachs, R. K. (Academic Press, New York); or Carter, B., and Bardeen, J. M. (1972). inBlack Holes, Proceedings of the Les Hauches Summer School ed. DeWitt, C., and DeWitt, B. S. (Gordon and Breach, New York).
- Islam, J. N. (1976).Math. Proc. Cambridge Phil. Soc.,79, 161.
- Weyl, H. (1917).Ann. Phys. Leipzig,54, 117.
- Lewis, T. (1932).Proc. R. Soc. London,A136, 176.
- Papapetrou, A. (1953).Ann. Phys. Leipzig,12, 309.
- Kerr, R. (1963).Phys. Rev. Lett.,11, 237.
- Tomimatsu, A., and Sato, H. (1973).Prog. Theor. Phys. (Kyoto),50, 95.
- On the existence of a general rotating solution of Einstein's equations
General Relativity and Gravitation
Volume 7, Issue 10 , pp 809-815
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- Industry Sectors
- Jamal N. Islam (1)
- Author Affiliations
- 1. Department of Applied Mathematics and Astronomy, University College, P.O. Box 78, CF1 1XL, Cardiff, UK